Backfaces give strange results with Fresnel Node in Cycles
If you use the Fresnel node that has an IOR, then this is the correct behaviour, as the IOR is computed taking the direction of the normal into account.

A quick solution would be to use the layer weight node and select "Facing". You can alter the effect using an RGB curves node afterwards. Fresnel is basically "Facing" with a blend of 0.5 and an exponential curve afterwards:



The example above uses exactly the same normal setup as you do, but by using "Facing" the flipped normal faces are treated the same as the regular ones.